Simplify the following expression: $t = \dfrac{40q + 64}{-64}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $40q + 64 = (2\cdot2\cdot2\cdot5 \cdot q) + (2\cdot2\cdot2\cdot2\cdot2\cdot2)$ The denominator can be factored: $-64 = - (2\cdot2\cdot2\cdot2\cdot2\cdot2)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $t = \dfrac{(8)(5q + 8)}{(8)(-8)}$ Dividing both the numerator and denominator by $8$ gives: $t = \dfrac{5q + 8}{-8}$